We consider a McKean-Vlasov system of kinetic type, where the equation is degenerate because the dimension of the driving Brownian motion is strictly smaller than that of the solution, as typically occurs in classical models of collisional kinetic theory. Assuming Hölder continuous coefficients and a weak Hörmander condition, we prove the well-posedness of the equation. Under stronger assumptions, we also show that the system propagates chaos.
Well-posedness and propagation of chaos for kinetic McKean-Vlasov equations
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